File:LogisticMap BifurcationDiagram.png
From Infogalactic: the planetary knowledge core
Size of this preview: 800 × 566 pixels. Other resolutions: 320 × 226 pixels | 1,838 × 1,300 pixels.
Original file (1,838 × 1,300 pixels, file size: 571 KB, MIME type: image/png)
Lua error in package.lua at line 80: module 'strict' not found.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 13:49, 3 January 2017 | | 1,838 × 1,300 (571 KB) | 127.0.0.1 (talk) | A <a href="https://en.wikipedia.org/wiki/Bifurcation_diagram" class="extiw" title="w:Bifurcation diagram"> bifurcation diagram</a> for the <a href="https://en.wikipedia.org/wiki/Logistic_map" class="extiw" title="w:Logistic map"> Logistic map</a>: <dl><dd><span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>r</mi><msub><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><mn>1</mn><mo>−<!-- − --></mo><msub><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi></mrow></msub><mo stretchy="false">)</mo><mspace width="thinmathspace"></mspace></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle x_{n+1}=rx_{n}(1-x_{n})\,}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a264267cc81cf50f8d905a9fc3e877a4c09022fa" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:20.222ex; height:2.843ex;" alt="{\displaystyle x_{n+1}=rx_{n}(1-x_{n})\,}"></span></dd></dl> The horizontal axis is the <i>r</i> parameter, the vertical axis is the <i>x</i> variable. The image was created by forming a 1601 x 1001 array representing increments of 0.001 in <i>r</i> and <i>x</i>. A starting value of <i>x</i>=0.25 was used, and the map was iterated 1000 times in order to stabilize the values of <i>x</i>. 100,000 <i>x</i> -values were then calculated for each value of <i>r</i> and for each <i>x</i> value, the corresponding <i>(x,r)</i> pixel in the image was incremented by one. All values in a column (corresponding to a particular value of <i>r</i>) were then multiplied by the number of non-zero pixels in that column, in order to even out the intensities. Values above 250,000 were set to 250,000, and then the entire image was normalized to 0-255. Finally, pixels for values of <i>r</i> below 3.57 were darkened to increase visibility. |
- You cannot overwrite this file.
File usage
The following 9 pages link to this file:
